Answer: [tex]a_{25} = 128[/tex]
Step-by-step explanation:
You need to use this formula:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where [tex]a_n[/tex] is the nth] term, [tex]a_1[/tex] is the first term,"n" is the term position and "d" is the common diference.
You must find the value of "d". Substitute [tex]a_1=8[/tex], [tex]a_9=48[/tex] and [tex]n=9[/tex] into the formula and solve for "d":
[tex]48 = 8 + (9 - 1)d\\48=8+8d\\48-8=8d\\40=8d\\d=5[/tex]
Now, you can calculate the 25th term substituting into the formula these values:
[tex]a_1=8[/tex]
[tex]d=5[/tex] and [tex]n=25[/tex]
Then you get:
[tex]a_{25} = 8 + (25 - 1)5[/tex]
[tex]a_{25} = 8 + 120[/tex]
[tex]a_{25} = 128[/tex]
